I agree that good judgement needs to be employed when deciding how to use this technique to solve a problem or if to use it at all. Perl does a great job of providing us many tools so that we can choose the right tool for the job. This basic tutorial was intended to introduce the concept and illustrate a basic example of the steps taken to transform a basic function into a Higher Order one.
With regards to extensibility and named parameters, the advantage is clear when you consider optional parameters using the positional approach. Imagine your function starts out accepting 3 parameters. You then add an optional parameter which you stick on the end. Now if you want to add a 5th parameter you need to change the ordering of the parameters which will break backwards compatability. The issue gets even more complicated if you have more than one optional parameter.
If this doesn't make my position clear, let me know and I will provide a concrete example using Tie::SortHash and Tie::Hash::Sorted.